Answer:
AC= 6 cm
Step-by-step explanation:
It is given that ABCD is a trapezoid
Also AC divides the trapezoid into two similar triangles
ΔABC≈ΔDCA
The ratio of corresponding sides of similar triangles are equal, so we have
[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now we can take
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
[tex]\frac{4}{AC} =\frac{AC}{9}[/tex] ( since BC=4 and AD= 9)
now we cross multiply
[tex]4(9)=AC^{2}[/tex]
[tex]AC^{2}=36[/tex]
[tex]AC=\sqrt{36}[/tex] (taking square root )
AC= 6 cm
